document.write( "Question 189153: This question came from an exam paper in Australia:
\n" ); document.write( "Solve: z^2=3+5i
\n" ); document.write( "I presume that the question requires an answer in the form z = a + bi
\n" ); document.write( "I have tried, but I end up getting a square root of a square root for an exact answer, or approx. +1.1897 or -1.1897 for b and approx. +2.1013 or -2.1013 for a.\r
\n" ); document.write( "\n" ); document.write( "I obtained this by letting z = a + bi, and therefore z^2 = a^2 + 2abi -b^2, and therefore a^2 - b^2 equals 3, and 2ab equals 5, and then solving these two simultaneous equations.\r
\n" ); document.write( "\n" ); document.write( "Is there a simpler way, please?
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #141898 by Alan3354(69443) $\"\"$ $\"About$

You can put this solution on YOUR website!
Use the Argand diagram.
\n" ); document.write( "--> = (34)^(1/4)cis(29.52)
\n" ); document.write( "= ~ 2.415cis(29.52)
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